The Ramsauer-Townsend effect

We have observed emission of $\mu t$ from a hydrogen layer into vacuum via imaging of muon decay electrons. From the position and time of the muon decay, the information on the energy distribution of the emitted $\mu t$ is obtained. Comparing the electron time spectrum in the vacuum region with detailed Monte Carlo calculations, we determined the Ramsauer-Townsend energy minimum to be eV, in agreement with the theoretical prediction of 12.4 eV by Chiccoli et al. using the multi-level calculations in the Adiabatic Representation of the three body Coulomb problem (the Nuclear Atlas [17]). Molecular and condensed matter effects are not included in our analysis, but their influence on $\mu t$ transport properties is expected to be negligible at these energies. Figure 9.1 illustrates the preferred variations (shaded band) of cross section from this measurement together with theoretical values (dashed line) [17]. Our results are consistent with the emission probability of about 15% per muon stopped in the production layer.

  

Figure 9.1: The preferred variations in $\mu t + p$ elastic scattering cross sections from this measurement (shown in a shaded band), together with the original theoretical cross sections from Ref. [17] (dashed line). The dot-dashed line is the constant cross sections used in the comparison given in Fig. 9.2. The box is an expansion near the Ramsauer-Townsend minimum plotted on a linear scale.

In addition to the above MWPC measurements from Run Series I, the $d\mu t$fusion measurements from Run Series II which were performed in a quite different setup (see Table 4.1) can add some information. A preliminary result of the time spectrum of fusion at the DS thick layer with no US moderation layer is consistent with the RT scaling of when all other nominal physics input, and the nominal US-DS target spacing, are assumed. Given the considerable difference in the setup and detection method, this gives us further confidence in our measurement of the RT minimum reported in this thesis.

We note that preliminary results of recent measurements [234] performed by our collaboration, but using a different X-ray technique and independent analysis with a separate MC, indicate a shift of the RT minimum ( eV, or relative 3% shift) to lower energy, opposite to the indication given here. It should be noted that not all uncertainties were included in the quoted value; for example, the error in the target spacing has been neglected so far. The difference between the X ray measurement and the MWPC measurement reported here probably gives a measure of unexpected systematic uncertainties. We stress, however, that for our goal of molecular formation rate measurements, the confirmation of the theoretical RT minimum energy at the 10% level is sufficient, in comparison with uncertainties in other processes.

  

Figure 9.2: The time spectrum of $\mu t$ decay in vacuum region (error bars) compared with a Monte Carlo calculation assuming no RT minimum in the $\mu t + p$ cross section (histogram). An energy independent cross section of cm² was assumed in the simulation, which gives a similar $\mu t$ yield in the vacuum region. The comparison clearly rules out the possibility of a constant cross section, establishing the existence of a minimum in $\mu t + p$ cross section.

Finally, we present in Fig. 9.2 a comparison of our MWPC emission data with a Monte Carlo calculation assuming no RT minimum. The simulation using an energy independent cross section of cm² gives a similar yield of $\mu t$ emitted in vacuum, but its time-of-flight distribution is very different. Thus our measurements provide direct evidence for the existence of a deep minimum in the $\mu t + p$ cross section. Note that in diffusion type measurements, which are mainly sensitive to the integrated diffusion length, it would be more difficult to rule out the possibility of an energy-independent cross section.